The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 1 1 X X 1 1 X 1 1 X 1 1 0 X 0 0 0 0 0 0 0 0 0 0 0 0 2X X 2X 2X 2X X X X 2X X 2X X X 0 X 0 2X X 0 X 0 2X X X 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X 2X 2X X 2X 0 X 2X 2X 0 X 0 2X X 2X X X 2X 2X X 0 0 0 X 2X 0 0 X 0 0 0 0 X 0 0 0 0 0 X X 2X 2X X X 2X 2X 2X X 2X 0 0 X 0 2X 0 2X 0 0 2X 2X 2X 0 0 X X X 2X X 2X X 0 0 0 0 0 X 0 0 0 X 2X 2X 2X X X 2X 2X 2X X 0 2X X 0 0 X X 2X 0 X 0 2X 0 0 0 2X 0 0 0 X 0 X 0 0 0 0 0 0 0 X 0 0 2X 2X X X 0 X X X 0 0 2X 2X X 2X X X X 2X 2X 0 X 0 2X 0 2X 2X X 2X 2X 0 0 0 2X 0 0 0 0 0 0 0 X 0 2X X 2X X 2X 0 0 2X 2X 2X 0 0 X X X 2X 0 X X X 0 X 2X X 0 X X X 2X 2X 2X X 2X 0 0 0 0 0 0 0 0 X X 0 X 0 X 2X 0 2X 2X 0 X 2X 2X X 0 X 0 0 X X X 0 X 2X 2X X 2X 2X 0 X X 0 X 0 generates a code of length 42 over Z3[X]/(X^2) who´s minimum homogenous weight is 63. Homogenous weight enumerator: w(x)=1x^0+40x^63+216x^66+308x^69+462x^72+718x^75+1654x^78+3588x^81+5158x^84+4188x^87+1884x^90+582x^93+424x^96+240x^99+128x^102+68x^105+20x^108+2x^111+2x^117 The gray image is a linear code over GF(3) with n=126, k=9 and d=63. This code was found by Heurico 1.16 in 6.03 seconds.